To convert radical to exponential form, let us first consider the equivalent form of radical.

Convert the radical form to exponential form :

Problem 1 :

(5√x)3

Solution :

5th root can be written as power 1/5.

(5√x)3 = (x1/5)3

To simplify the term, which is having a power raised to another power, we can multiply the powers.

(5√x)= x(1/5) x 3

= x3/5

Problem 2 :

(3√y4)

Solution :

Cube root can be written as power 1/3.

(3√y4) = (y4)1/3

= y4/3

Problem 3 :

(√x5)

Solution :

Square root can be written as power 1/2.

(√x5) = (x5)1/2

= x5/2

Problem 4 :

(3√5)3

Solution :

Cube root can be written as power 1/3.

(3√5)3 = (5(1/3))3

= 53/3

= 5

Problem 5 :

√(16x2)

Solution :

Square root can be written as power 1/2.

√(16x2) = (16x2)1/2

16 can be written as 42

√(16x2) = (42x2)1/2

= ((4x)2)1/2

= (4x) (1/2)

= 4x

Problem 6 :

1/(√(6x))3

Solution :

Square root can be written as power 1/2.

1/(√(6x))3 = 1/[(6x)1/2]3

= 1/(6x)(1/2) x 3

= 1/(6x)(3/2)

When we move the term from numerator to denominator or denominator to numerator, we have to change the sign of the power.

= (6x)-3/2

Problem 7 :

1/(4√x)7

Solution :

Fourth root can be written as power 1/4.

1/(4√x)7 = 1/(x1/4)7

= 1/x(1/4⋅ 7

= 1/x(7/4)

= x-7/4

Problem 8 :

1/√(5x)

Solution :

Square root can be written as power 1/2.

1/√(5x) = 1/(5x)1/2

= (5x)-1/2

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